Defining parameters
| Level: | \( N \) | = | \( 729 = 3^{6} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(39366\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(729))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 660 | 330 | 330 |
| Cusp forms | 12 | 6 | 6 |
| Eisenstein series | 648 | 324 | 324 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(729))\)
We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 729.1.b | \(\chi_{729}(728, \cdot)\) | None | 0 | 1 |
| 729.1.d | \(\chi_{729}(242, \cdot)\) | None | 0 | 2 |
| 729.1.f | \(\chi_{729}(80, \cdot)\) | 729.1.f.a | 6 | 6 |
| 729.1.h | \(\chi_{729}(26, \cdot)\) | None | 0 | 18 |
| 729.1.j | \(\chi_{729}(8, \cdot)\) | None | 0 | 54 |
| 729.1.l | \(\chi_{729}(2, \cdot)\) | None | 0 | 162 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(729))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(729)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 2}\)